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Linear combination of images



Z = imlincomb(K1,A1,K2,A2,...,Kn,An) computes the linear combination of images, A1, A2, … , An, with weights K1, K2, … , Kn according to:

Z = K1*A1 + K2*A2 + ... + Kn*An


Z = imlincomb(K1,A1,K2,A2,...,Kn,An,K) adds an offset, K, to the linear combination:

Z = K1*A1 + K2*A2 + ... + Kn*An + K


Z = imlincomb(___,outputClass) specifies the output class of Z.


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Read an image into the workspace.

I = imread('cameraman.tif');

Scale the image using a coefficient of 1.5 in the linear combination.

J = imlincomb(1.5,I);

Display the original image and the processed image.



Read an image into the workspace.

I = imread('cameraman.tif');

Create a low-pass filtered copy of the image.

J = uint8(filter2(fspecial('gaussian'), I));

Find the difference image and shift the zero value to 128 using a linear combination of I and J.

K = imlincomb(1,I,-1,J,128); %K(r,c) = I(r,c) - J(r,c) + 128

Display the resulting difference image.


Read two grayscale uint8 images into the workspace.

I = imread('rice.png');
J = imread('cameraman.tif');

Add the images using a linear combination. Specify the output as type uint16 to avoid truncating the result.

K = imlincomb(1,I,1,J,'uint16');

Display the result.


This example shows the difference between nesting calls and using linear combinations when performing a series of arithmetic operations on images. To illustrate how imlincomb performs all the arithmetic operations before truncating the result, compare the results of calculating the average of two arrays, X and Y, using nested arithmetic functions and using imlincomb.

Create two arrays.

X = uint8([ 255 0 75; 44 225 100]);
Y = uint8([ 50 50 50; 50 50 50 ]);

Average the arrays using nested arithmetic functions. To calculate the average returned in Z(1,1), the function imadd adds 255 and 50 and truncates the result to 255 before passing it to imdivide. The average returned in Z(1,1) is 128.

Z = imdivide(imadd(X,Y),2)
Z = 2x3 uint8 matrix

   128    25    63
    47   128    75

In contrast, imlincomb performs the addition and division in double precision and only truncates the final result. The average returned in Z2(1,1) is 153.

Z2 = imlincomb(.5,X,.5,Y)
Z2 = 2x3 uint8 matrix

   153    25    63
    47   138    75

Input Arguments

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Image coefficients, specified as numeric scalars.

Data Types: double

Input images, specified as numeric arrays of the same size and class.

Offset, specified as a numeric scalar.

Data Types: double

Output class of Z, specified as a string scalar or character vector containing the name of a numeric class.

Example: 'uint16'

Example: "double"

Output Arguments

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Linearly combined image, returned as a numeric array of the same size as A1. If A1 is logical, then Z is double, otherwise Z has the same class as A1.


  • When performing a series of arithmetic operations on a pair of images, you can achieve more accurate results if you use imlincomb to combine the operations, rather than nesting calls to the individual arithmetic functions, such as imadd. When you nest calls to the arithmetic functions, and the input arrays are of an integer class, each function truncates and rounds the result before passing it to the next function, thus losing accuracy in the final result. imlincomb computes each element of the output Z individually, in double-precision floating point. If Z is an integer array, imlincomb clips elements of Z that exceed the range of the integer type and rounds off fractional values.

Extended Capabilities

Version History

Introduced before R2006a

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